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    "# 08 - 工具变量\n",
    "\n",
    "## 绕过省略变量偏差（OVB）\n",
    "\n",
    "控制OVB的一种方法是，将省略的变量添加到我们的模型中。但是，这并不总是可行的，主要是因为我们根本没有关于省略变量的数据。例如，让我们回到教育对工资影响的模型：\n",
    "\n",
    "$\n",
    "\\log(hwage)_i = \\beta_0 + \\kappa \\ educ_i + \\pmb{\\beta} Ability_i + u_i\n",
    "$\n",
    "\n",
    "为了弄清楚教育对 \\\\( \\log(hwage)\\\\)的因果效应 \\\\(\\kappa\\\\)，我们需要控制能力因素\\\\(Ability_i\\\\)。如果我们不这样做，我们可能会有一些偏差，毕竟，能力可能是一个混淆因子，同时影响干预变量：教育，以及结果变量：收入。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "from matplotlib import style\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "import statsmodels.formula.api as smf\n",
    "import graphviz as gr\n",
    "from linearmodels.iv import IV2SLS\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "pd.set_option(\"display.max_columns\", 5)\n",
    "style.use(\"fivethirtyeight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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    "g = gr.Digraph()\n",
    "\n",
    "g.edge(\"能力\", \"教育\")\n",
    "g.edge(\"能力\", \"工资\")\n",
    "g.edge(\"教育\", \"工资\")\n",
    "g"
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   "cell_type": "markdown",
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   "source": [
    "避免这种情况的一种方法是在衡量教育对工资的影响时控制恒定的能力水平。我们可以通过在线性回归模型中包含能力来做到这一点。但是，我们没有很好的能力衡量标准。我们拥有的最好的是一些非常可疑的近似变量，比如智商。\n",
    "\n",
    "但并不是完全没有办法。这是工具变量进入我们视野的地方。IV的想法是找到导致干预的另一个变量，并且它仅通过干预和结果相关。换一种说法就是，此工具变量 \\\\(Z_i\\\\) 与 \\\\(Y_0\\\\) 不相关，但它与 \\\\(T\\\\) 相关。有时这个被称为排除限制（exclusion restriction）。"
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    "g = gr.Digraph()\n",
    "\n",
    "g.edge(\"能力\", \"教育\")\n",
    "g.edge(\"能力\", \"工资\")\n",
    "g.edge(\"教育\", \"工资\")\n",
    "g.edge(\"工具变量\", \"教育\")\n",
    "g"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果我们有这样的变量，我们可以用我们将看到的 IV 公式恢复因果效应 \\\\(\\kappa\\\\)。为此，让我们考虑一下我们想要运行的理想方程。使用更一般的术语，如 \\\\(T\\\\) 干预变量和 \\\\(W\\\\) 混淆因子，下面的公式就是我们想要的：\n",
    "\n",
    "$\n",
    "Y_i = \\beta_0 + \\kappa \\ T_i + \\pmb{\\beta}W_i + u_i\n",
    "$\n",
    "\n",
    "但是，我们没有关于 \\\\(W\\\\) 的数据，所以我们只能运行\n",
    "\n",
    "$\n",
    "Y_i = \\beta_0 + \\kappa\\ T_i + v_i\n",
    "$\n",
    "\n",
    "$\n",
    "v_i = \\pmb{\\beta}W_i + u_i\n",
    "$\n",
    "\n",
    "由于 \\\\(W\\\\) 是一个混淆因子，所以 \\\\(Cov(T, v) \\neq 0\\\\)。我们有一个短而不长的等式。在我们的示例中，这意味着能力与教育相关。如果是这种情况，由于省略了变量，运行短回归将产生 \\\\(\\kappa\\\\) 的有偏估计量。\n",
    "\n",
    "现在，看看 IV 的魔力吧！由于工具 \\\\(Z\\\\) 仅与通过 \\\\(T\\\\) 的结果相关，这意味着 \\\\(Cov(Z,v) = 0\\\\)，否则会有从 \\\\(Z\\\\) 到 \\\\(Y\\\\) 到 \\\\(W\\\\) 的第二条路径。考虑到这一点，我们可以写\n",
    "\n",
    "$\n",
    "Cov(Z,Y) = Cov(Z,\\beta_0 + \\kappa\\ T_i + v_i) = \\kappa Cov(Z,T) + Cov(Z, v) = \\kappa Cov(Z,T)\n",
    "$\n",
    "\n",
    "将每一边除以 \\\\(V(Z_i)\\\\) 并重新排列项，我们得到\n",
    "\n",
    "$\n",
    "\\kappa = \\dfrac{Cov(Y_i, Z_i)/V(Z_i)}{Cov(T_i, Z_i)/V(Z_i)} = \\dfrac{\\text{Reduced Form}}{\\text{1st Stage}}\n",
    "$\n",
    "\n",
    "请注意，分子和分母都是回归系数（协方差除以方差）。分子是 Y 对 Z 的回归结果。换句话说，它是 Z 对 Y 的“影响”。请记住，这并不是说 Z 导致 Y，因为我们要求 Z 仅通过T。相反，它只是捕捉 Z 对 Y 到 T 的这种影响有多大。这个分子非常有名，它有自己的名字：简化形式系数。\n",
    "\n",
    "分母也是回归系数。这次是T对Z的回归。这个回归捕捉到Z对T的影响是什么，它也非常有名，被称为第一阶段系数。\n",
    "\n",
    "看待这个方程的另一种很酷的方式是偏导数。我们可以证明 T 对 Y 的影响等于 Z 对 Y 的影响，按 Z 对 T 的影响进行缩放：\n",
    "\n",
    "$\n",
    "\\kappa = \\dfrac{\\frac{\\partial y}{\\partial z}}{\\frac{\\partial T}{\\partial z}} = \\dfrac{\\partial y}{\\partial z} * \\dfrac{ \\partial z}{\\partial T} = \\dfrac{\\partial y}{\\partial T}\n",
    "$\n",
    "\n",
    "这向我们展示的东西比大多数人所欣赏的更微妙。它也比大多数人想象的要凉爽。通过这样写 IV，我们是在说，“看，由于混杂因素，很难找到 T 对 Y 的影响。但我可以很容易地找到 Z 对 Y 的影响，因为没有任何东西导致 Z 和 Y（排除限制）。但是，我感兴趣的是 T 对 Y 的影响，而不是 Z 对 Y 的影响。因此，我将估计 Z 对 Y 的简单影响，并通过 Z 对 T 的影响**缩放它**，将效果转换为 T 单位而不是 Z 单位”。\n",
    "\n",
    "我们也可以在工具是虚拟变量的简化情况下看到这一点。在这种情况下，IV 估计量通过 2 个均值差异之间的比率得到进一步简化。\n",
    "\n",
    "$\n",
    "\\kappa = \\dfrac{E[Y|Z=1]-E[Y|Z=0]}{E[T|Z=1]-E[T|Z=0]}\n",
    "$\n",
    "\n",
    "这个比率有时被称为**Wald Estimator**。同样，我们可以告诉 IV 故事我们想要 T 对 Y 的影响，这很难得到。所以我们专注于 Z 对 Y 的影响，这很容易。根据定义，Z 仅通过 T 影响 Y，因此我们现在可以将 Z 对 Y 的影响转换为 T 对 Y 的影响。我们通过 Z 对 T 的影响缩放 Z 对 Y 的影响来实现。\n",
    "\n",
    "## 出生季度和教育对工资的影响\n",
    "\n",
    "到目前为止，我们一直将这些工具视为一些神奇的变量 \\\\(Z\\\\)，它们具有仅通过干预变量影响结果的神奇特性。老实说，好的工具变量来之不易，我们不妨将它们视为奇迹。让我们说它不适合胆小的人。有传言说，芝加哥经济学院的酷孩子们谈论他们是如何在酒吧里想出这种或那种工具变量的。\n",
    "\n",
    "![img](./data/img/iv/good-iv.png)\n",
    "\n",
    "不过，我们确实有一些有趣的工具示例，可以让事情变得更具体一些。我们将再次尝试估计教育对工资的影响。为此，我们将使用该人的出生季度作为工具 Z。\n",
    "\n",
    "这个想法利用了美国强制出勤法。通常，他们声明孩子必须在他们入学当年的 1 月 1 日之前满 6 岁。因此，年初出生的孩子入学年龄较大。强制出勤法还要求学生在学校上学直到他们年满 16 岁，届时他们在法律上被允许退学。结果是，与年初出生的人相比，年末出生的人平均受教育年限更长。\n",
    "\n",
    "![img](./data/img/iv/qob.png)\n",
    "\n",
    "如果我们接受出生季度与能力因素无关，即它不会混淆教育对工资的影响，我们可以将其用作工具。换句话说，我们需要相信出生季度对工资没有影响，除了对教育的影响。如果你不相信占星术，这是一个非常有说服力的论点。"
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       "<g id=\"edge2\" class=\"edge\"><title>能力&#45;&gt;工资</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M129.819,-143.871C125.026,-119.564 116.203,-74.8187 110.523,-46.0132\"/>\r\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"113.954,-45.3232 108.586,-36.1893 107.086,-46.6775 113.954,-45.3232\"/>\r\n",
       "</g>\r\n",
       "<!-- 教育&#45;&gt;工资 -->\r\n",
       "<g id=\"edge3\" class=\"edge\"><title>教育&#45;&gt;工资</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M84.5947,-72.411C87.7097,-64.3352 91.5298,-54.4312 95.0307,-45.3547\"/>\r\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"98.3225,-46.5458 98.6558,-35.9562 91.7915,-44.0267 98.3225,-46.5458\"/>\r\n",
       "</g>\r\n",
       "<!-- 出生季度 -->\r\n",
       "<g id=\"node4\" class=\"node\"><title>出生季度</title>\r\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"44.1961\" cy=\"-162\" rx=\"44.393\" ry=\"18\"/>\r\n",
       "<text text-anchor=\"middle\" x=\"44.1961\" y=\"-158.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">出生季度</text>\r\n",
       "</g>\r\n",
       "<!-- 出生季度&#45;&gt;教育 -->\r\n",
       "<g id=\"edge4\" class=\"edge\"><title>出生季度&#45;&gt;教育</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M52.4265,-144.055C56.4523,-135.767 61.3817,-125.618 65.8472,-116.424\"/>\r\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"69.0547,-117.831 70.2755,-107.307 62.7582,-114.773 69.0547,-117.831\"/>\r\n",
       "</g>\r\n",
       "</g>\r\n",
       "</svg>\r\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x233f221bbc8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = gr.Digraph()\n",
    "\n",
    "g.edge(\"能力\", \"教育\")\n",
    "g.edge(\"能力\", \"工资\")\n",
    "g.edge(\"教育\", \"工资\")\n",
    "g.edge(\"出生季度\", \"教育\")\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为了进行这种分析，我们可以使用来自三次十年一次的人口普查的数据，这些数据与[Angrist和Krueger](https://economics.mit.edu/faculty/angrist/data1/data/angkru1991) 在他们关于IV的文章中使用的数据相同。该数据集包含有关我们的结果变量，即工资取对数的结果，以及我们的干预变量，即受教育年限的信息。它还包含我们的工具变量，即出生季度，以及其他控制变量的数据，例如出生年份和出生状态。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>log_wage</th>\n",
       "      <th>years_of_schooling</th>\n",
       "      <th>year_of_birth</th>\n",
       "      <th>quarter_of_birth</th>\n",
       "      <th>state_of_birth</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.790019</td>\n",
       "      <td>12.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.952494</td>\n",
       "      <td>11.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.315949</td>\n",
       "      <td>12.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.595926</td>\n",
       "      <td>12.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.068915</td>\n",
       "      <td>12.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   log_wage  years_of_schooling  year_of_birth  quarter_of_birth  \\\n",
       "0  5.790019                12.0           30.0               1.0   \n",
       "1  5.952494                11.0           30.0               1.0   \n",
       "2  5.315949                12.0           30.0               1.0   \n",
       "3  5.595926                12.0           30.0               1.0   \n",
       "4  6.068915                12.0           30.0               1.0   \n",
       "\n",
       "   state_of_birth  \n",
       "0            45.0  \n",
       "1            45.0  \n",
       "2            45.0  \n",
       "3            45.0  \n",
       "4            37.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"./data/ak91.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第一阶段\n",
    "\n",
    "在我们使用出生季度作为工具变量之前，我们需要确保它是有效的。这意味着我们支持工具变量的两个假设：\n",
    "\n",
    "1. \\\\(Cov(Z， T) \\neq 0 \\\\)。这是说我们应该有一个强大的第一阶段，或者工具变量确实会影响干预变量。\n",
    "2. \\\\(Y \\perp Z |T \\\\).这是排除限制，声明工具变量Z仅通过干预T影响结果Y。\n",
    "\n",
    "幸运的是，第一个假设是可以验证的。我们从数据中可以看出\\\\(Cov(Z， T)\\\\)不为零。在我们的例子中，如果出生的季度确实是一个工具变量，就像我们所说的那样，我们应该期望在一年中最后一个季度出生的人比年初出生的人有更多的受教育时间。在运行任何统计测试来验证这一点之前，让我们绘制我们的数据并亲眼看到它。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "group_data = (data\n",
    "              .groupby([\"year_of_birth\", \"quarter_of_birth\"])\n",
    "              [[\"log_wage\", \"years_of_schooling\"]]\n",
    "              .mean()\n",
    "              .reset_index()\n",
    "              .assign(time_of_birth = lambda d: d[\"year_of_birth\"] + (d[\"quarter_of_birth\"])/4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,6))\n",
    "plt.plot(group_data[\"time_of_birth\"], group_data[\"years_of_schooling\"], zorder=-1)\n",
    "for q in range(1, 5):\n",
    "    x = group_data.query(f\"quarter_of_birth=={q}\")[\"time_of_birth\"]\n",
    "    y = group_data.query(f\"quarter_of_birth=={q}\")[\"years_of_schooling\"]\n",
    "    plt.scatter(x, y, marker=\"s\", s=200, c=f\"C{q}\")\n",
    "    plt.scatter(x, y, marker=f\"${q}$\", s=100, c=f\"white\")\n",
    "\n",
    "plt.title(\"Years of Education by Quarter of Birth (first stage)\")\n",
    "plt.xlabel(\"Year of Birth\")\n",
    "plt.ylabel(\"Years of Schooling\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "值得注意的是，在一年中的四分之一之后，学校教育的年份有一个季节性的模式。从图形上我们可以看到，一年中第一季度出生的人的受教育程度几乎总是低于最后一个季度出生的人（毕竟，一旦我们控制了出生年份，那些晚年出生的人通常受教育程度更高）。\n",
    "\n",
    "为了更严格一点，我们可以将第一阶段作为线性回归运行。我们首先将出生季度转换为虚拟变量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>log_wage</th>\n",
       "      <th>years_of_schooling</th>\n",
       "      <th>...</th>\n",
       "      <th>q3</th>\n",
       "      <th>q4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.790019</td>\n",
       "      <td>12.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.952494</td>\n",
       "      <td>11.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.315949</td>\n",
       "      <td>12.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.595926</td>\n",
       "      <td>12.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.068915</td>\n",
       "      <td>12.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   log_wage  years_of_schooling  ...  q3  q4\n",
       "0  5.790019                12.0  ...   0   0\n",
       "1  5.952494                11.0  ...   0   0\n",
       "2  5.315949                12.0  ...   0   0\n",
       "3  5.595926                12.0  ...   0   0\n",
       "4  6.068915                12.0  ...   0   0\n",
       "\n",
       "[5 rows x 9 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor_data = data.assign(**{f\"q{int(q)}\": (data[\"quarter_of_birth\"] == q).astype(int)\n",
    "                             for q in data[\"quarter_of_birth\"].unique()})\n",
    "\n",
    "factor_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为简单起见，现在只使用最后一个季度，即Q4，作为工具。我们将使用干预变量：受教育年限，对工具变量：出生季度，进行回归。这将向我们展示出生在哪个季度是否确实像我们在上图中看到的那样对教育时间产生了积极影响。我们还需要在这里控制出生年份，我们将添加出生状态作为额外的控制。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q4 parameter estimate:,  0.10085809272785906\n",
      "q4 p-value:,  5.464829416638474e-15\n"
     ]
    }
   ],
   "source": [
    "first_stage = smf.ols(\"years_of_schooling ~ C(year_of_birth) + C(state_of_birth) + q4\", data=factor_data).fit()\n",
    "\n",
    "print(\"q4 parameter estimate:, \", first_stage.params[\"q4\"])\n",
    "print(\"q4 p-value:, \", first_stage.pvalues[\"q4\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "看起来，在一年中最后一个季度出生的人平均比在一年中其他季度出生的人多受教育0.1年。p 值接近于零。这结束了关于出生在哪个季度是否导致更多或更少受教育年限的案例。\n",
    "\n",
    "![免疫接种](./data/img/iv/incomplete-files.png)\n",
    "\n",
    "## 简化形式\n",
    "\n",
    "不幸的是，我们无法验证第二种IV条件。我们只能支持它。我们可以表达我们的信念，即出生四分之一不会影响潜在的收入。换句话说，人们出生的时间并不表示他们的个人能力或任何其他可能导致收入差异的因素，除了对教育的影响。一个好方法是说，当我们考虑出生季度对收入的影响时，出生季度与随机分配一样好。（它不是随机的。有证据表明，人们倾向于在夏末或某种假期前后怀孕。但我想不出任何充分的理由表明这种模式也会以除教育以外的任何方式影响收入）。\n",
    "\n",
    "\n",
    "在支持排除限制之后，我们可以继续运行简化形式。简化的形式旨在弄清楚工具变量如何影响结果。从假设出发，因为所有这些影响都是基于对干预的影响，这将为干预如何影响结果提供一些启示。让我们在认真对待回归之前，再一次直观地认识这一点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,6))\n",
    "plt.plot(group_data[\"time_of_birth\"], group_data[\"log_wage\"], zorder=-1)\n",
    "for q in range(1, 5):\n",
    "    x = group_data.query(f\"quarter_of_birth=={q}\")[\"time_of_birth\"]\n",
    "    y = group_data.query(f\"quarter_of_birth=={q}\")[\"log_wage\"]\n",
    "    plt.scatter(x, y, marker=\"s\", s=200, c=f\"C{q}\")\n",
    "    plt.scatter(x, y, marker=f\"${q}$\", s=100, c=f\"white\")\n",
    "\n",
    "plt.title(\"Average Weekly Wage by Quarter of Birth (reduced form)\")\n",
    "plt.xlabel(\"Year of Birth\")\n",
    "plt.ylabel(\"Log Weekly Earnings\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们再一次可以看到出生季度与收入的季节性关系。当年晚些时候出生的人的收入略高于年初出生的人。为了验证这个假设，我们将再次在对数工资上对工具变量Q4进行回归。我们还将添加与第 1 阶段相同的附加控制变量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q4 parameter estimate:,  0.008603484260138683\n",
      "q4 p-value:,  0.0014949127183684287\n"
     ]
    }
   ],
   "source": [
    "reduced_form = smf.ols(\"log_wage ~ C(year_of_birth) + C(state_of_birth) + q4\", data=factor_data).fit()\n",
    "\n",
    "print(\"q4 parameter estimate:, \", reduced_form.params[\"q4\"])\n",
    "print(\"q4 p-value:, \", reduced_form.pvalues[\"q4\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们再次取得了显著的结果。那些出生在每年最后一个季度的人，平均工资高出0.8%。这一次，p值不像以前那样接近于零，但它仍然非常重要，仅为0.0015。\n",
    "\n",
    "## 手动工具变量\n",
    "\n",
    "有了我们的简化形式和第一阶段，我们现在可以通过简化形式来缩放第一阶段的效果。由于第一阶段系数约为0.1，这将使减少的形式系数的影响乘以近10。这将给我们对平均因果效应的无偏见的IV估计：\n",
    "\n",
    "\n",
    "$\n",
    "ATE_{IV} = \\dfrac{\\text{Reduced Form}}{\\text{1st Stage}} \n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08530286492084561"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reduced_form.params[\"q4\"] / first_stage.params[\"q4\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这意味着我们应该期望每增加一年的学费就会增加8%。\n",
    "\n",
    "获得IV估计值的另一种方法是使用2个阶段最小二乘法**2SLS**。通过此过程，我们像以前一样执行第一阶段，然后运行第二阶段，其中我们用第一阶段的拟合值替换处理变量\n",
    "\n",
    "$\n",
    "educ_i = gamma_0 + gamma_1 * q4_i + gamma_2 yob_i + gamma_3 sob_i + v_i\n",
    "$\n",
    "\n",
    "$\n",
    "log（wage）_i = beta_0 + beta_1 educ_i + beta_2 yob_i + beta_3 sob_i + u_i\n",
    "$\n",
    "\n",
    "$\n",
    "log（wage）_i = beta_0 + beta_1 [gamma_0 + gamma_1 * q4_i + gamma_2 yob_i + gamma_3 sob_i + v_i ] + beta_2 yob_i + beta_3 sob_i + u_i\n",
    "$\n",
    "\n",
    "需要注意的一点是，**我们在执行IV**时，我们添加到第二阶段的任何其他控制变量也应添加到第一阶段**。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08530286492116357"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iv_by_hand = smf.ols(\"log_wage ~ C(year_of_birth) + C(state_of_birth) + years_of_schooling_fitted\",\n",
    "                     data=factor_data.assign(years_of_schooling_fitted=first_stage.fittedvalues)).fit()\n",
    "\n",
    "iv_by_hand.params[\"years_of_schooling_fitted\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如您所见，参数完全相同。第二种看待IV的方式对于它给出的直觉是有用的。在2SLS中，第一阶段创建一个新版本的干预变量，该版本从省略的变量偏置中清除。然后，我们在线性回归中使用这种清除版本的处理，即第一阶段的拟合值。 \n",
    "\n",
    "然而，在实践中，我们不会手工做IV。不是因为它很麻烦，而是因为我们从第二阶段得到的标准错误有点偏差。相反，我们应该总是让机器为我们完成工作。在Python中，我们可以使用[linearmodels](https://bashtage.github.io/linearmodels/)软件包 以正确的方式运行2SLS。\n",
    "\n",
    "\n",
    "2SLS的公式有点不同。我们应该在公式中添加第一阶段回归公式 [ ] 之间的部分。在我们的例子中，我们添加了\"years_of_schooling~ q4\"。不需要将其他控制变量添加到第一阶段，因为如果我们在第二阶段中包含其他控制变量，计算机将自动执行此操作。出于这个原因，我们在第一阶段的公式之外添加了\"year_of_birth\"和\"state_of_birth\"。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: 0.0853028649235057\n",
      "SE: 0.025540812814298396\n",
      "95 CI: [0.03524287 0.13536286]\n",
      "P-value: 0.0008381914659547629\n"
     ]
    }
   ],
   "source": [
    "def parse(model, exog=\"years_of_schooling\"):\n",
    "    param = model.params[exog]\n",
    "    se = model.std_errors[exog]\n",
    "    p_val = model.pvalues[exog]\n",
    "    print(f\"Parameter: {param}\")\n",
    "    print(f\"SE: {se}\")\n",
    "    print(f\"95 CI: {(-1.96*se,1.96*se) + param}\")\n",
    "    print(f\"P-value: {p_val}\")\n",
    "    \n",
    "formula = 'log_wage ~ 1 + C(year_of_birth) + C(state_of_birth) + [years_of_schooling ~ q4]'\n",
    "iv2sls = IV2SLS.from_formula(formula, factor_data).fit()\n",
    "parse(iv2sls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以看到，该参数与我们之前的参数又是完全相同的。额外的好处是，我们现在有有效的标准差。有了这个，我们可以说，我们预计额外1年的教育平均而言将增加8.5%的工资。\n",
    "\n",
    "## 多个工具变量\n",
    "\n",
    "使用计算机的另一个优点是用于运行2SLS估计法，因为它很容易添加多个工具变量。在我们的示例中，我们将使用所有以出生季度标定的虚拟变量作为学校教育年限水平的工具变量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: 0.10769370488969798\n",
      "SE: 0.019557149009493794\n",
      "95 CI: [0.06936169 0.14602572]\n",
      "P-value: 3.657974678716869e-08\n"
     ]
    }
   ],
   "source": [
    "formula = 'log_wage ~ 1 + C(year_of_birth) + C(state_of_birth) + [years_of_schooling ~ q1+q2+q3]'\n",
    "iv_many_zs = IV2SLS.from_formula(formula, factor_data).fit()\n",
    "parse(iv_many_zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于所有3个虚拟变量，估计的教育回报率现在是0.1，这意味着我们应该期望每增加一年的教育收入平均增长10%。让我们将其与传统的 OLS 估计值进行比较。为此，我们可以再次使用2SLS，但现在没有第一阶段。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: 0.06732572817657978\n",
      "SE: 0.00038839984390486563\n",
      "95 CI: [0.06656446 0.06808699]\n",
      "P-value: 0.0\n"
     ]
    }
   ],
   "source": [
    "formula = \"log_wage ~ years_of_schooling + C(state_of_birth) + C(year_of_birth) + C(quarter_of_birth)\"\n",
    "ols = IV2SLS.from_formula(formula, data=data).fit()\n",
    "parse(ols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "据估计，OLS的教育回报率低于2SLS。这表明OVB可能不像我们第一次那么强大。另外，请注意置信区间。2SLS 的 CI 比 OLS 估计值宽得多。让我们进一步探讨一下\n",
    "\n",
    "## 工具变量的弱点\n",
    "\n",
    "![免疫接种](./data/img/iv/weak-iv.png)\n",
    "\n",
    "在处理IV时，我们需要记住我们是间接估计ATE的。我们的估计取决于第一阶段和第二阶段。如果干预对结果的影响确实很强，那么第二阶段也会很强。但是，如果我们的第一阶段很弱，那么第二阶段有多强并不重要。弱的第一阶段意味着工具变量与干预的相关性非常小。因此，我们无法从工具变量中学到太多有关干预的知识。\n",
    "\n",
    "\n",
    "IV标准误差的公式有点复杂，不那么直观，所以我们将尝试其他东西来掌握这个问题。我们将模拟数据，其中我们的干预 T 对结果 Y 的影响为2.0，未观察到的混淆变量 U 和额外的对照 X。我们还将在第一阶段模拟具有不同优势的多种工具变量。\n",
    "\n",
    "$\n",
    "X \\sim N(0, 2^2)\\\\\n",
    "U \\sim N(0, 2^2) \\\\\n",
    "T \\sim N(1+0.5U, 5^2) \\\\\n",
    "Y \\sim N(2+ X - 0.5U + 2T， 5^2)\\\\\n",
    "Z \\sim N(T, sigma^2) \\text{  for }\\sigma^2 \\text{ in 0.1 to 100}\\\\\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>U</th>\n",
       "      <th>T</th>\n",
       "      <th>...</th>\n",
       "      <th>Z_48</th>\n",
       "      <th>Z_49</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.696148</td>\n",
       "      <td>8.056988</td>\n",
       "      <td>...</td>\n",
       "      <td>-117.798705</td>\n",
       "      <td>-13.485292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.570240</td>\n",
       "      <td>0.245067</td>\n",
       "      <td>...</td>\n",
       "      <td>-209.727577</td>\n",
       "      <td>-70.792948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.664741</td>\n",
       "      <td>5.597510</td>\n",
       "      <td>...</td>\n",
       "      <td>60.562232</td>\n",
       "      <td>47.619414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.037725</td>\n",
       "      <td>0.493532</td>\n",
       "      <td>...</td>\n",
       "      <td>78.136513</td>\n",
       "      <td>-108.322304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.590591</td>\n",
       "      <td>-6.263014</td>\n",
       "      <td>...</td>\n",
       "      <td>78.776566</td>\n",
       "      <td>-80.547214</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 53 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          U         T  ...        Z_48        Z_49\n",
       "0  2.696148  8.056988  ... -117.798705  -13.485292\n",
       "1  2.570240  0.245067  ... -209.727577  -70.792948\n",
       "2  0.664741  5.597510  ...   60.562232   47.619414\n",
       "3  1.037725  0.493532  ...   78.136513 -108.322304\n",
       "4 -2.590591 -6.263014  ...   78.776566  -80.547214\n",
       "\n",
       "[5 rows x 53 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(12)\n",
    "n = 10000\n",
    "X = np.random.normal(0, 2, n) # observable variable\n",
    "U = np.random.normal(0, 2, n) # unobservable (omitted) variable\n",
    "T = np.random.normal(1 + 0.5*U, 5, n) # treatment\n",
    "Y = np.random.normal(2 + X - 0.5*U + 2*T, 5, n) # outcome\n",
    "\n",
    "stddevs = np.linspace(0.1, 100, 50)\n",
    "Zs = {f\"Z_{z}\": np.random.normal(T, s, n) for z, s in enumerate(stddevs)} # instruments with decreasing Cov(Z, T)\n",
    "\n",
    "sim_data = pd.DataFrame(dict(U=U, T=T, Y=Y)).assign(**Zs)\n",
    "\n",
    "sim_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "仔细检查一下，我们可以看到Z和T之间的相关性确实在下降。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Z_0    0.999807\n",
       "Z_1    0.919713\n",
       "Z_2    0.773434\n",
       "Z_3    0.634614\n",
       "Z_4    0.523719\n",
       "Name: T, dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corr = (sim_data.corr()[\"T\"]\n",
    "        [lambda d: d.index.str.startswith(\"Z\")])\n",
    "\n",
    "corr.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在，我们将为每个工具变量运行一个IV模型，并收集ATE估计值和标准误差。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "se = []\n",
    "ate = []\n",
    "for z in range(len(Zs)):\n",
    "    formula = f'Y ~ 1 + X + [T ~ Z_{z}]'\n",
    "    iv = IV2SLS.from_formula(formula, sim_data).fit()\n",
    "    se.append(iv.std_errors[\"T\"])\n",
    "    ate.append(iv.params[\"T\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data = pd.DataFrame(dict(se=se, ate=ate, corr=corr)).sort_values(by=\"corr\")\n",
    "\n",
    "plt.scatter(plot_data[\"corr\"], plot_data[\"se\"])\n",
    "plt.xlabel(\"Corr(Z, T)\")\n",
    "plt.ylabel(\"IV Standard Error\");\n",
    "plt.title(\"Variance of the IV Estimates by 1st Stage Strength\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(plot_data[\"corr\"], plot_data[\"ate\"])\n",
    "plt.fill_between(plot_data[\"corr\"],\n",
    "                 plot_data[\"ate\"]+1.96*plot_data[\"se\"],\n",
    "                 plot_data[\"ate\"]-1.96*plot_data[\"se\"], alpha=.5)\n",
    "plt.xlabel(\"Corr(Z, T)\")\n",
    "plt.ylabel(\"$\\hat{ATE}$\");\n",
    "plt.title(\"IV ATE Estimates by 1st Stage Strength\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "正如我们在上面的图中看到的那样，当 \\\\(T\\\\) 和 \\\\(Z\\\\) 之间的相关性较弱时，估计值会有很大差异。这是因为当相关性较低时，SE也会增加很多。\n",
    "\n",
    "另一件需要注意的事情是**2SLS是有偏的**！即使相关性很高，参数估计值仍未达到 2.0 的真实 ATE。实际上，2.0 甚至不在 95% 的 CI 中！2SLS 仅一致，这意味着如果样本数量足够大，它将接近真实参数值。但是，我们不知道多大才足够大。我们只能坚持一些经验法则来理解这种偏见的行为方式：\n",
    "\n",
    "\n",
    "1. 2SLS 偏向于 OLS。这意味着，如果 OLS 具有负/正偏差，则 2SLS 也将具有该偏差。2SLS 的优点是，在省略变量的情况下，它至少是一致的，而 OLS 则不是。在上面的例子中，我们未观察到的U对结果产生负面影响，但与干预呈正相关，这将导致负面偏见。这就是为什么我们看到ATE估计值低于真实值（负偏差）。。\n",
    "\n",
    "2. 偏差将随着我们添加的工具数量而增加。如果我们添加太多的工具，2SLS变得越来越像OLS。\n",
    "\n",
    "除了知道这种偏差的行为方式之外，最后一条建议是避免在**做IV时出现一些常见错误**：\n",
    "\n",
    "1. 手工做IV。正如我们所看到的，即使参数估计是正确的，手动IV也会导致错误的标准误差。SE 不会完全关闭。不过，如果您可以使用软件并获得正确的SE，为什么要这样做呢？\n",
    "\n",
    "2. 在第一阶段使用OLS以外的任何东西。许多数据科学家遇到IV并认为他们可以做得更好。例如，他们看到一个虚拟的处理，并考虑用逻辑回归替换第一阶段，毕竟，他们正在预测一个虚拟变量，对吧？问题是，这显然是错误的。IV 的一致性依赖于只有 OLS 才能给出的属性，即残差的正交性，因此在第 1 阶段与 OLS 不同的任何内容都会产生偏差。（OBS：有一些现代技术使用机器学习进行IV，但它们的结果充其量是值得怀疑的）。\n",
    "\n",
    "## 关键思想\n",
    "\n",
    "我们在这里花了一些时间来理解如果我们有一个工具变量，我们如何解决省略的变量偏差。工具变量是与干预相关的变量（具有第一阶段），但仅通过干预（排除限制）影响结果。我们看到一个以分季度的出生率作为工具变量的例子，用于估计教育对收入的影响。\n",
    "\n",
    "然后，我们深入研究使用IV估计因果效应的机制，即使用2SLS。我们还了解到，IV不是银弹。当我们的第一阶段很弱时，这可能会很麻烦。此外，尽管一致，但2SLS仍然是估计因果效应的有偏方法。"
   ]
  }
 ],
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